Multiply (6 cis 300^{o})(2 cis 30^{o}) and express the answer in rectangular form.

I know how to express this in polar form, but how do I put it into rectangular form?

Shades
Dec 3, 2015

#1**+15 **

Hi Shades :)

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form. {nl} {nl} I know how to express this in polar form, but how do I put it into rectangular form?

\( (6 e^{300^{0}i})*(2e^{30^0i})\\~\\ =12e^{330^0i}\\~\\ =12(cos330+isin330)\\~\\ =12(cos30-isin30))\\~\\ =12(\frac{\sqrt3}{2}-i*\frac{1}{2})\\~\\ =6\sqrt3-6i\)

Melody
Dec 3, 2015

#1**+15 **

Best Answer

Hi Shades :)

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form. {nl} {nl} I know how to express this in polar form, but how do I put it into rectangular form?

\( (6 e^{300^{0}i})*(2e^{30^0i})\\~\\ =12e^{330^0i}\\~\\ =12(cos330+isin330)\\~\\ =12(cos30-isin30))\\~\\ =12(\frac{\sqrt3}{2}-i*\frac{1}{2})\\~\\ =6\sqrt3-6i\)

Melody
Dec 3, 2015

#3**+5 **

You are very welcome Shades :)

You probably already have a good text book but I found this online. Maybe it will be helpful.

https://www.adelaide.edu.au/mathslearning/bridging/resources/MT5ComplexBook_Feb2013.pdf

Melody
Dec 3, 2015